EP2828044B1 - Trajectory generation device, moving object, trajectory generation method - Google Patents

Trajectory generation device, moving object, trajectory generation method Download PDF

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Publication number
EP2828044B1
EP2828044B1 EP13716375.4A EP13716375A EP2828044B1 EP 2828044 B1 EP2828044 B1 EP 2828044B1 EP 13716375 A EP13716375 A EP 13716375A EP 2828044 B1 EP2828044 B1 EP 2828044B1
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Prior art keywords
trajectory
trajectories
evaluation
longest
generation device
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German (de)
English (en)
French (fr)
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EP2828044A1 (en
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Koji Terada
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Toyota Motor Corp
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Toyota Motor Corp
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • B25J9/1666—Avoiding collision or forbidden zones
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/0003—Home robots, i.e. small robots for domestic use
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0214—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory in accordance with safety or protection criteria, e.g. avoiding hazardous areas
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/40—Robotics, robotics mapping to robotics vision
    • G05B2219/40428—Using rapidly exploring random trees algorithm RRT-algorithm
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/40—Robotics, robotics mapping to robotics vision
    • G05B2219/40431—Grid of preoptimised paths as function of target position, choose closest, fine adapt
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/40—Robotics, robotics mapping to robotics vision
    • G05B2219/40512—Real time path planning, trajectory generation
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/40—Robotics, robotics mapping to robotics vision
    • G05B2219/40516—Replanning
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/40—Robotics, robotics mapping to robotics vision
    • G05B2219/40519—Motion, trajectory planning
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10S901/00—Robots
    • Y10S901/01—Mobile robot
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10S901/00—Robots
    • Y10S901/02—Arm motion controller

Definitions

  • the invention relates to a trajectory generation device that generates a trajectory of a moving object such as a robot, a moving object and a trajectory generation method.
  • the trajectory generation of a robot arm is, for example, a search problem of about 6th to 20th dimensions that involves mathematical difficulty.
  • the motion planning of a robot designed for use in the home environment is complex and, as the environment is constantly changing, the motion planning becomes more difficult.
  • a trajectory generation method in which a state with the smallest distance to a target state is selected from the states registered as the branches of a known-state registration tree and, from the selected state, a trajectory is calculated (see Japanese Patent Application Publication No. 2011-161624 ( JP 2011-161624 A )).
  • this document does not disclose at least a trajectory generation device comprising a trajectory generation unit that calculates a longest trajectory part, which is present in a moving object moving area in a trajectory acquired by a trajectory acquisition unit, and generates a connection trajectory by connecting both ends of the calculated longest trajectory part to a predetermined start point and a predetermined end point respectively
  • JP 2011-161624 A JP 2011-161624 A
  • the present invention provides a trajectory generation device that generates a trajectory of a moving object more efficiently, a moving object and a trajectory generation method.
  • a first aspect of the invention is a trajectory generation device characterized by including a storage unit that stores a plurality of trajectories; a trajectory acquisition unit that acquires a trajectory, corresponding to an environment similar to a current environment, from the plurality of trajectories stored in the storage unit; and a trajectory generation unit that calculates a longest trajectory part, which is present in a moving object moving area excluding an obstacle area in the current environment, when said trajectory acquired by the trajectory acquisition unit is applied to the current environment, and generates a trajectory by connecting both ends of the calculated longest trajectory part to a predetermined start point and a predetermined end point respectively.
  • the trajectory generation unit may calculate a longest trajectory part that is present in a moving object moving area excluding an obstacle area and that satisfies a predetermined restriction condition, connect branches, one extending from the predetermined start point and another extending from the predetermined end point, to both ends of the calculated longest trajectory part respectively using a Rapidly-Exploring Random Tree (RRT) method, and generates the trajectory in a final form by smoothing the connected trajectory.
  • the storage unit may store the trajectory and an evaluation of the trajectory and the trajectory acquisition unit may acquire a trajectory, which corresponds to an environment similar to the current environment and is highly evaluated, from the plurality of trajectories stored in the storage unit.
  • the trajectory generation unit may calculate a longest trajectory part, which is present in a moving object moving area in each of a plurality of the trajectories acquired by the trajectory acquisition unit, generate trajectories, one for each of the plurality of acquired trajectories, by connecting both ends of the calculated longest trajectory part to a predetermined start point and a predetermined end point, evaluate each of the generated trajectories, and determine a final trajectory based on the evaluation of the trajectories.
  • the evaluation may include at least one of an evaluation of a path length, an evaluation of a distance from an obstacle, an evaluation of consumption energy at a movement time, and an evaluation of user sensitivity.
  • a moving object that includes the trajectory generation device wherein the moving object moves based on a trajectory generated by the trajectory generation device.
  • another aspect of the present invention is a trajectory generation method characterized by including acquiring a trajectory, corresponding to an environment similar to a current environment, from a plurality of trajectories stored in a storage unit; and calculating a longest trajectory part, which is present in a moving object moving area excluding an obstacle area in the current environment, when said acquired trajectory is applied to the current environment, and generating a trajectory by connecting both ends of the calculated longest trajectory part to a predetermined start point and a predetermined end point respectively.
  • the present invention can provide a trajectory generation device that generates a trajectory of a moving object more efficiently, a moving object, and a trajectory generation method.
  • FIG. 1 is a block diagram showing a general system configuration of a trajectory generation device in one embodiment of the present invention.
  • a trajectory generation device 1 in this embodiment which generates a trajectory of a moving object such as a robot or a robot arm, is mounted on a moving object.
  • a moving object, such as a robot, moves according to a trajectory generated by the trajectory generation device 1.
  • the trajectory generation device 1 includes a trajectory database 2 that stores a plurality of trajectories in advance, a reference trajectory acquisition unit 3 that acquires a reference trajectory from the trajectory database 2, and a differential motion generation unit 4 that generates a trajectory based on an acquired reference trajectory.
  • the hardware of the trajectory generation device 1 is configured mainly by a microcomputer.
  • the microcomputer includes a central processing unit (CPU) that performs control processing and operation processing, a read only memory (ROM) that stores a control program and an operation program executed by the CPU, and a random access memory (RAM) that temporarily stores data to be processed.
  • the CPU, ROM, and RAM are interconnected by a data bus.
  • the trajectory database 2 is configured by the ROM or RAM described above.
  • the trajectory database 2 stores a plurality of trajectories each represented in the form of a correspondence among a motion planning input for an arm motion planning problem of a robot, a motion planning output, and the evaluation of the motion planning output.
  • the arm motion planning problem refers to a problem that receives an input (motion planning input), such as environment information, a robot model, a restriction condition, and a basic planning condition necessary for a robot to perform a desired motion, and calculates time-series data on the joint angles (motion planning output) necessary for an actual robot motion.
  • the environment information is information based on a model, information based on actual data, or a combination of these two types of information.
  • the information based on a model refers to information by which the shape can be clearly recognized in advance by drawings, for example, data on a position/pose and an object type.
  • the information based on actual data refers to information in which voxels, obtained by a 3D sensor, are used as environment data.
  • the robot model described above includes kinematics information (joint position relation, axial direction), geometric information (robot shape, etc.,) and dynamics information (weight, maximum torque, etc.).
  • the restriction condition described above includes a holding object (object held in the planning), a tilting restriction (orientation of hands for holding a holding object), an output torque (maximum output torque of a motor), and robot position/pose (position and pose of a robot in the environment).
  • the basic planning condition includes an initial joint angle, a terminal joint angle, and a robot position/pose.
  • the motion planning output which is time-series data on the joint angles necessary for the robot to actually move, is expressed by expression (1) given below.
  • [Math. 1] ⁇ ⁇ R n ⁇ ⁇ t 0 , ⁇ t 1 , ⁇ , ⁇ t m
  • ⁇ is a joint angle vector
  • n is the number of joints
  • ⁇ is an arm trajectory
  • t is a time
  • m is the number of trajectories.
  • Each time arm motion planning is performed (each time an arm motion problem is solved), a correspondence among a motion planning input to the arm motion planning problem, a motion planning output, and the evaluation of the motion planning output is stored in the trajectory database 2 automatically or by the user.
  • the reference trajectory acquisition unit 3 acquires a trajectory, which corresponds to an environment similar to the current environment, from a plurality of trajectories stored in the trajectory database 2. For example, as the initial value of the arm motion planning problem to be solved, the reference trajectory acquisition unit 3 selects a trajectory from the trajectory database 2.
  • the trajectory selected in this case is a trajectory whose motion planning input (for example, the current environment such as the position/pose of robot, object type, and object position) is similar to that of the arm motion planning problem to be solved and whose motion planning output is highly evaluated.
  • the reference trajectory acquisition unit 3 outputs the selected trajectory to the differential motion generation unit 4 as a reference trajectory.
  • a trajectory whose environment is similar to the current environment and whose output is highly evaluated, is stored in the trajectory database 2 in advance, using such a trajectory enables efficient trajectory generation.
  • the following describes in detail a method used by the reference trajectory acquisition unit 3 to compare the two motion planning inputs, one is the motion planning input of an arm motion planning problem to be solved and the other is a motion planning input stored in the trajectory database 2 and, based on the comparison result, select a trajectory, corresponding to the motion planning input most similar to that of the arm motion planning problem to be solved, from the trajectory database 2.
  • the reference trajectory acquisition unit 3 uses the function given below to compare the position/pose of a robot between the two motion planning inputs.
  • the position/pose of a robot in the motion planning input is represented by expression (2) given below, for example, using a quaternion, while the position/pose of an object is represented by expression (3) given below.
  • T robot _ initial x y z r x r y r z r w
  • T objectXX _ pos x y z r x r y r z r w
  • L pose T 1 T 2 w p ⁇ p 1 ⁇ p 2 ⁇ + w r ⁇ angle r 1 r 2 ⁇
  • T 1 is the position/pose to be compared
  • T 2 is the position/pose to compare
  • p 1 is parallel position of T 1
  • p 2 is the parallel position of T 2
  • r 1 is the quaternion of T 1
  • r 2 is the quaternion of T 2
  • w p is the weight on parallel translation
  • w r is the weight on the rotation direction
  • angle0 is the function that returns the rotation angle between the two quaternions.
  • the reference trajectory acquisition unit 3 compares the robot's environment information between the two motion planning inputs using the functions represented by expression (5) and expression (6) given below.
  • the reference trajectory acquisition unit 3 uses expression (5) given below to compare the object presence vector O, which represents what object is in the environment using 1 and 0, and to compare the pose of each object, between the two motion planning inputs.
  • a representation for example, the sofa is near the chair
  • L env O 1 O 2 ⁇ i ! O 1 i ⁇ O 2 i
  • O 1 is the object presence vector to be compared and O 2 is the object presence vector to compare.
  • the reference trajectory acquisition unit 3 uses expression (6) given below for the comparison by directly using vectors.
  • the reference trajectory acquisition unit 3 may also use the integrated value (number of units) of voxels or a feature extracted value, such as flatness, for the comparison.
  • L env B 1 B 2 ⁇ B 1 , B 2 ⁇
  • B 1 and B 2 each indicate the vector of a voxel.
  • the reference trajectory acquisition unit 3 uses expression (7), which indicates the similarity of the motion planning inputs, to compare the motion planning input of the arm motion planning problem to be solved and the motion planning input stored in the trajectory database 2 to select the most similar motion planning input.
  • I 1 is the motion planning input of the arm motion planning problem to be solved
  • I 2 is the motion planning input stored in the trajectory database 2.
  • the reference trajectory acquisition unit 3 selects a similar motion planning input, whose calculated value of expression (7) is smallest (that is, highest similarity), from the trajectory database 2.
  • the similarity may also be calculated by multiplying the similarity in each restriction condition by a weight and then cumulatively adding up the resulting values or by multiplying the similarity in the robot model by a weight and then cumulatively adding up the resulting values. This enables the similarity between the motion planning inputs to be calculated more accurately.
  • the arm may mistakenly collide with an obstacle due to a recognition error or a modeling error. Considering this, it is also possible to give a better evaluation when the evaluation of the nearest point to an obstacle is higher.
  • a lower consumption energy required for an arm operation has a merit that the consumption power is reduced.
  • the evaluation of the total energy required for arm trajectory generation may be added to the evaluation of the path-integrated value described above.
  • the user's sensitivity evaluation, or a combination of any evaluations described above may be added to the evaluation of the path-integrated value described above. Adding these factors to the evaluation increases the accuracy of the evaluation.
  • FIG. 2 is a flowchart showing a method used by the reference trajectory acquisition unit 3 for selecting a trajectory, whose motion planning input is similar to the motion planning input of an arm motion planning problem to be solved and whose evaluation of the motion planning output is high, from the trajectory database 2.
  • the reference trajectory acquisition unit 3 sets the motion planning input to I r (step S101), sets the initial value of parameter i to 0 (step S102), and increments parameter i by 1 (step S103).
  • the reference trajectory acquisition unit 3 acquires motion planning input I i , and motion planning output O i from the trajectory database 2 (step S105). On the other hand, if it is determined that parameter i is equal to or larger than the number of pieces of data stored in the trajectory database 2 (NO in step S104), the reference trajectory acquisition unit 3 terminates the processing.
  • the reference trajectory acquisition unit 3 determines whether the similarity L input (I r , I i ) is larger than the predetermined value L min and the evaluation value E (O i ) is larger than the threshold (step S106). If it is determined that the similarity L input (I r , I i ) is larger than the predetermined value L min and the evaluation value E (O i ) is larger than the threshold (YES in step S106), the reference trajectory acquisition unit 3 assigns the value of parameter i to min and to L min and then returns control to the above processing (step S103).
  • the differential motion generation unit 4 one example of a trajectory - generation unit, performs differential processing described below based on the reference trajectory (motion planning output, i.e., an approximate trajectory for the arm motion planning problem to be solved) acquired from the reference trajectory acquisition unit 3 and generates a new trajectory.
  • motion planning output i.e., an approximate trajectory for the arm motion planning problem to be solved
  • the differential motion generation unit 4 uses the Differential Bi-Directional Rapidly-Exploring Random Tree (DBiRRT) method (hereinafter simply called RRT method) that is an extended version of RRT-Connect. Using this method, the differential motion generation unit 4 extracts a longest possible trajectory part from the trajectory, acquired by the reference trajectory acquisition unit 3, to efficiently generate a trajectory.
  • DBiRRT Differential Bi-Directional Rapidly-Exploring Random Tree
  • the differential motion generation unit 4 calculates a longest trajectory part that is present in the robot moving area excluding an obstacle area and that satisfies a predetermined restriction condition. Then, the differential motion generation unit 4 uses the RRT method to connect the branches, one extending from the start point and the other extending from the end point, to each of the both ends of the calculated longest trajectory part and smoothes the connected trajectory to generate the final trajectory.
  • the trajectory generation method according to the DBiRRT method is described in detail below.
  • the differential motion generation unit 4 acquires a reference trajectory from the reference trajectory acquisition unit 3 ( FIG. 3A ).
  • the differential motion generation unit 4 applies the reference trajectory, acquired from the reference trajectory acquisition unit 3, to the arm motion planning problem to be solved ( FIG. 3B ).
  • the robot cannot move along the reference trajectory. This is because there are new obstacles associated with the arm motion planning problem to be solved and because the start point and the end point of the acquired reference trajectory differ respectively from the start point and the end point of the arm motion planning problem to be solved.
  • the differential motion generation unit 4 calculates the longest trajectory part T'longest. (trajectory part included in the dotted-line frame) that is present in a robot moving area excluding the obstacle area and that satisfies a predetermined restriction condition (for example, maximum or minimum joint angle, maximum joint torque, etc.) ( FIG. 3C ).
  • a predetermined restriction condition for example, maximum or minimum joint angle, maximum joint torque, etc.
  • the differential motion generation unit 4 extends the branches, one extending from the start point and the other extending from the end point, using the BiRRT method and connects them respectively to the ends of the calculated trajectory part T'longest ( FIG. 4A ).
  • the differential motion generation unit 4 determines the trajectory, generated by the connection described above, as a temporarily solved trajectory ( FIG. 4B ).
  • the differential motion generation unit 4 smoothes the temporarily solved trajectory to make it shorter and determines the smoothed trajectory as the finally solved trajectory ( FIG. 4C ).
  • the differential motion generation unit 4 performs the differential processing as described above and generates a new trajectory to generate a reliable trajectory quickly.
  • the reference trajectory acquisition unit 3 may select a plurality of trajectories as reference trajectories, each corresponding to a motion planning input similar to the motion planning input of the arm motion planning problem to be solved and each corresponding to a highly-evaluated motion planning output, from the trajectory database 2.
  • the differential motion generation unit 4 performs the differential processing for the plurality of reference trajectories, acquired by the reference trajectory acquisition unit 3, as described above to generate a plurality of trajectories. After that, the differential motion generation unit 4 evaluates each generated trajectory as described above to determine the final trajectory.
  • the differential motion generation unit 4 may instantly determine a trajectory, which is one of the generated trajectories and is selected first, as the final trajectory. This generation method may be used to generate a trajectory more quickly in a complex environment. The differential motion generation unit 4 may also determine a trajectory, which is one of the generated trajectories and whose evaluation value is highest, as the final trajectory. This generation method may be used to generate a more optimal trajectory. In addition, the differential motion generation unit 4 may determine a trajectory, which is one of the generated trajectories and whose evaluation value is higher, than a predetermined value, as the final trajectory. This generation method may be used to generate a trajectory with a certain level of evaluation while reducing the trajectory generation time.
  • the reference trajectory acquisition unit 3 of the trajectory generation device 1 acquires a reference trajectory, whose motion planning input is similar to the motion planning input of the motion planning problem to be solved and whose motion planning output is highly evaluated, from the trajectory database 2.
  • the differential motion generation unit 4 calculates the longest trajectory part that is in the robot moving area excluding the obstacle area and satisfies a predetermined restriction condition.
  • the differential motion generation unit 4 connects the branches, one extending from a predetermined start point and the other extending from a predetermined end point, to the both ends of the calculated longest trajectory part respectively to generate a final trajectory. In this way, the trajectory generation device 1 can generate the trajectory of a moving object more efficiently.
  • the present invention is not limited thereto.
  • the present invention may also be implemented by causing the CPU to execute the processing of the reference trajectory acquisition unit 3 and the differential motion generation unit 4.
  • the program may be stored in various types of non-transitory computer readable medium for distribution to a computer.
  • a non-transitory computer readable medium includes various types of tangible storage medium. Examples of a non-transitory computer readable storage medium include a magnetic recording medium (for example, flexible disk, magnetic tape, hard disk drive), a magneto optic recording medium (for example, optical magnetic disc), a compact disc read only memory (CD-ROM), a CD recordable (CD-R), a CD-ReWritable (CD-R/W), and a semiconductor memory (for example, mask ROM, programmable ROM (PROM), Erasable PROM (EPROM), flash ROM, and random access memory (RAM)).
  • a magnetic recording medium for example, flexible disk, magnetic tape, hard disk drive
  • a magneto optic recording medium for example, optical magnetic disc
  • CD-ROM compact disc read only memory
  • CD-R CD recordable
  • CD-ReWritable CD-ReWritable
  • semiconductor memory for example, mask ROM, programmable ROM
  • the program may also be distributed to a computer via various types of transitory computer readable medium.
  • Examples of transitory computer readable medium include electric signals, optical signals, and electromagnetic waves.
  • a transitory computer readable medium allows the program to be distributed to a computer via a wired communication line such as an electric wire and an optical fiber or via a wireless communication line.
  • the present invention is applicable, for example, to a trajectory generation device that quickly generates a trajectory of a moving object such as a robot arm.

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  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Manipulator (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
  • Numerical Control (AREA)
EP13716375.4A 2012-03-22 2013-03-14 Trajectory generation device, moving object, trajectory generation method Active EP2828044B1 (en)

Applications Claiming Priority (2)

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JP2012065697A JP5724919B2 (ja) 2012-03-22 2012-03-22 軌道生成装置、移動体、軌道生成方法及びプログラム
PCT/IB2013/000529 WO2013140236A1 (en) 2012-03-22 2013-03-14 Trajectory generation device, moving object, trajectory generation method

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